Digital signal processors have previously selectively utilized both linear and logarithmic number representations in an effort to perform signal processing as fast and efficiently as possible. For example, finite impulse response (FIR) filters have been implemented by using logarithms to perform multiplication and division operations which can be readily accomplished by only adding and subtracting, respectively, numbers in logarithmic representation. However, addition and subtraction operations are much more complicated to perform in a logarithmic system rather than in a linear number system. Therefore, others have typically converted from logarithmic to linear to perform addition and then, if necessary, back to a logarithmic number representation to accomplish a multiplication or division operation. By effecting numerous conversions of number systems, the inherent advantages of the logarithmic number representation with respect to multiplication and division operations are typically lost.
A use of logarithmic signal processing includes a logarithmic multiplier and a logarithmic adder which utilize a bypass bus to bypass the adder when an input operand is zero. Because the number zero is not representable by logarithms and must be represented by a predetermined quantized minimum value, a bypass path typically couples the nonzero adder input operand directly from an adder input to an output thereof. Otherwise, the adder circuit will add the nonzero operand with a quantized minimum value to provide an output having a quantization error. A problem with such a logarithmic multiplier/adder is that the bypass path creates an additional bus which adds size and complexity to the general circuitry. Circuits which perform repetitive accumulations or multiply/accumulation operations generate operands having a bit size greater than the bit size of the operands. Typical processors do not have the ability to effect repetitive operations without losing extra bits generated each calculation during repetitive operations. Further, previous logarithmic adders and subtractors have typically used a look-up table containing a complete table of logarithmic values which function in a manner analogous to manually locating a linear value corresponding to a logarithmic value and adding or subtracting the linear values. Such look-up tables require very large ROMs to implement a complete table of logarithms and antilogarithms.